Basic Ohm s Law & Series and Parallel Circuits


 Jeffery Jennings
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1 2:256 Let there be no compulsion in religion: Truth stands out clear from Error: whoever rejects evil and believes in Allah hath grasped the most trustworthy handhold that never breaks. And Allah heareth and knoweth all things. Experiment 1 Basic Ohm s Law & Series and Parallel Circuits Test (a): Resistor Color Code Aims: To determine the value of resistors from their Electronic Industries Association (EIA) color code. To investigate the properties of potentiometer. Apparatus: Digital Multimeter. Resistors : R1=150Ω, R2=20kΩ and R3=5.1MΩ Linear 10kΩ potentiometer Background: Resistor The ohm is the unit of resistance, and it is represented by the symbol Ω (Greek letter omega). Resistance values are indicated by a standard color code that manufacturers have adopted. This code uses color band on the body of resistor. The colors and their numerical values are given in the resistor color chart, Table 1a1. This code is used for 1/8w, 1/4w, 1/2 w, 2w, and 3w resistors.(w stands for watt, i.e.is the power dissipation ability of the resistance). The basic resistor is shown in Figure 1a1. The standard color code marking consists of four bands around the body of the resistor. The color of the first band indicates the first significant figure of the resistance value. The second band indicates the second significant figure. The color of the third band indicates the number of zeros that follow the first two significant figures. For example: 1kΩ color codes are arranged from the leftmost to the rightmost to be brown, black, red and gold. The fourth band indicates the percent tolerance of the resistance. Percent tolerance in the amount the resistance may vary from the value indicated by the color code. Because resistors are mass produced, variations in materials will affect their actual resistance. Many circuits can still operate as designed even if the resistors in the circuit do not have the precise value specified. Tolerances are usually given as plus or minus the nominal, or color code value. Wire wound, highwattage resistors usually are not color coded but have the resistance value and
2 wattage rating printed on the body of resistor. To avoid having to write all the zeros for high value resistors the metric abbreviations of k (for 1000) and M for ( ) are used. For example: 33,000 Ω can be written as 33kΩ. (pronounced 33 kay, or 33 kilohms) 1,200,000 Ω can be written as 1.2MΩ. (Pronounced 1.2 meg, or 1.2 megohms). Color Significant figure (First & second band) No. of Zeros (Multiplier) (third band) %Tolerance (Forth band) Black 0 0(10 0 )  Brown 1 1(10 1 )  Red 2 2(10 2 )  Orange 3 3(10 3 )  Yellow 4 4(10 4 )  Green 5 5(10 5 )  Blue 6 6(10 6 )  Violet 7 7(10 7 )  Gray 8 8(10 8 )  White 9 9(10 9 )  Gold  1(101 ) 5 Silver  2(102 ) 10 No color Table 1a1: Resistor color code Lead First significant bit Second significant bit Tolerance No. of zeros Figure 1a1: resistor color code Variable resistors In addition to the fixedvalue resistors, variable resistors are used. The two types of variable resistors are the rheostat and the potentiometer. Volume controls used in radio is a typical example of potentiometer. A rheostat is essentially a twoterminal device. Its circuit symbol is shown in Figure 1a2. Points a and b are connected to the circuit. A rheostat has a maximum resistance value, specified by the manufacturer, and a minimum value, usually 0Ω. The arrow head indicates a mechanical means of adjusting the rheostat so that the resistance, measured between points a and b, can be adjusted to any intermediate value within the range of variation.
3 Figure 1a2 The circuit symbol of potentiometer, Figure 1a3, shows that this is a threeterminal device. The resistance between the terminals a and c is fixed. Point b is the variable arm of the potentiometer, the wiper. The arm is a metal contactor that slides along the uninsulated surface of the resistance element. The resistance between points a and c varies as the length of element included between points a and b. The same is true for points c and b. Figure 1a3 A potentiometer may be used as a rheostat if the center arm and one of the end terminals are connected into the circuit and the other end terminal is left disconnected. Method: Resistor color code: 1. The color code on each resistor defines the nominal value about which the tolerance is defined. The nominal value is that value of resistance that the resistor would have if its tolerance were 0 percent. Use the color code to determine the nominal value for each resistor and record them in Table 1a Determine the tolerance and record the values for each of the resistor. 3. Determine the theoretical maximum and minimum values for each resistor in turn. 4. Measure and record the actual value of resistor, and check to see whether or not this value falls between the calculated limits in step 2. Variable resistor: 1. Identify the end terminals and the wiper terminal for the potentiometer. Number them 1, 2 and 3 with 2 being the wiper. 2. Position the ohmmeter between terminals 12, 23 and 13 and record these measured values in Table 1a Add the values measured between terminals 12 and 23 and compare the result with the value measured between 13 (theoretical value). 4. Reposition the shaft of the potentiometer and repeat steps 2 and 3 for the other two trials.
4 Test (b): Voltage and Current Measurements Aim: To measure voltage and current in DC circuit. Apparatus: DC voltage supply, 2k resistor, and two Digital Multimeters (2DMMs). Background: The test will familiarize you with the basic voltage and current measurements that is connected to a dc power supply. Voltage Measurements A voltemeter must always be connected with probes across the component under test; that is, the circuit need never be broken (see Figure 1b1). This is often referred to as parallel connection. Polarity: It is a good practice to place the correct leads at the proper nodes. Eg. Red lead at the positive node and the black lead at the negative node. Current Measurements In measuring current (Figure 1b2), the meter must always be inserted within the circuit in such a manner that the current to be measured will flow through the meter and it is similar to a series connection. You must break the circuit to perform a current measurement. Figure 1b1 Figure 1b2 Figure 1b3
5 Method: 1. Switch on the power supply and set for the minimum output voltage. 2. Set the digital multimeter to measure voltage. 3. Connect the voltmeter directly to the power supply terminals. 4. Observe the effect of tuning the output voltage control and adjust the voltage value to 2 Volts. 5. Remove the meter and connect 2kΩ resistor across the terminals of the power supply as shown in Figure 1b1. Reconnect the meter as shown. Observe the value measured by the meter. 6. Now break the circuit as shown in 1b2 and insert the other meter set on ma current range. The meter will now be reading the current flowing in the circuit. 7. Record the current in Table 1b Increase the voltage in 2Volt steps. For each of the voltage increment, measure and record the current changes. Test (c): Ohm s Law Aim: To verify Ohm s law (V=IR). Apparatus: Voltage dc supply, resistors 5.1kΩ and two digital DMMs. Background: Ohm s Law is the basis of many electrical circuit calculations which indicates V=IR. In this experiment Ohms Law has to be verified and will prove that the current through a resistor is proportional to the voltage across it. The way in which we accomplish this is to measure the voltage across and the current through a known resistor for several different pairs of values. Data can then be plotted on a graph, and if the relationship is truly linear, it should yield a straight line. Figure 1c1 Method: 1. Measure the actual value of the resistor R and record the result in Table 1c Connect the circuit in Figure 1c1 with R= 5.1kΩ. 3. Beginning at 0 volt, increase the voltage across R in 1Volt steps until 9 Volts. Measure and record the resulting current in Table 1c1 for each increment of voltage. 4. Plot the graphs of I verses V for results in Table 1c1. (Assign I to the vertical axis and V to the horizontal axis). 5. Construct a right triangle on the graph and from this, redetermine the slope and hence evaluate
6 the conductance G. 6. From this information, evaluate the resistance R. Record G and R for the graph in the appropriate column in Table 1c Compare these experimentally obtained values with those measured values recorded in the respective tables. Analysis, deductions and conclusion: 1. Has Ohm s law been verified? 2. What are the facts supporting this decision? 3. State the factors affecting resistance of a material with a uniform crosssectional area? 4. What are the common types of fixed and variable resistors? State usage of each type. 5. If the Resistor from the experiment above is changed to 10kΩ, deduct what will happen to the slope of IV graph. What effect on the conductance G? 6. Do all resistors obey ohm s law? Justify your answer by stating some examples. Test (d): Series and Parallel Circuits Aims: To verify that in a series circuit; 1) The total resistance is equal to the sum of the individual resistors. 2) The voltage drops across the resistors equals to the applied voltage. 3) The value of the current is the same in all parts of the circuit. To verify that in parallel circuits; 1) The equivalent resistance is the reciprocal of the sum of reciprocals of the individual resistors. 2) The branch current in parallel equal to the supply current. 3) The voltage drop across each resistor in parallel is the same. To verify by measurement and calculation for two different networks: the total current and the branch values, the voltage drop across various parts of the networks and the method for determining the equivalent resistance of such networks. Apparatus: 15 volt dc supply. Two digital multimeters. Resistors ; 1.0kΩ, 1.5kΩ, 6.8kΩ Circuit Diagram: Figure 1d1
7 (a) Series Circuit Method: 1. Connect the circuit shown in Figure 1d Adjust the supply voltage to 15V.(Note the value must be kept constant throughout the test by connecting voltmeter across the voltage supply in the circuit to observe the voltage.) 3. Switch off the supply. Connect the ammeter in position A. 4. Switch on the supply. Read the current through resistor R1. 5. Connect the voltmeter across R1 and measure the voltage drop across it. 6. Repeat 3 until 5 for the ammeter positions B, C, and D and the voltmeter positions across resistors R2, and R3. 7. Record the voltage for close and open loop. Fill up the measured values in Table 1d1 (b) Parallel Circuits Circuit Diagram: Figure 1d2 Method: 1. Connect the circuit shown in Figure 1d Adjust the supply voltage 15V.(Note the value of the supply voltage and keep it constant throughout the test.) 3. Switch off the supply. Connect the ammeter in position A, the total current, I Total. Switch on the supply. Read the current through resistor R1 and the voltage drop across it. 4. Repeat 4 for the ammeter positions B, C, and D and the voltmeter positions across resistors R2, and R3. Be careful not to touch R3 during measurement as it might be hot. 5. Fill up the measured values in Table 1d2. Analysis, deductions and conclusions: 1. Have the aims been achieved? 2. What are the facts supporting these decision for each point of the aim? 3. What are the probable factors, which contributed to the discrepancies in the results for each point of the aim? 4. Indicate which circuit the principle of voltage division and current division is applicable to. 5. State the formula for each condition.
8 Table of Results Resistor R1 R2 R3 Nominal Value Tolerance % Maximum Value Minimum Value Measured Value Table 1a2 1 st trial 2 nd trial 3 rd trial R12 R23 R13 R12+R23 Table 1a3 V supply (volt) Current (Measured) Current (Calculated) Table 1b1 Nominal Resistance R=5.1kΩ Voltage Source (Vs) Current (Measured values) Current (Theoretical values) Measured Resistance R = (V) Table 1c1
9 Slope (G) R (1/G) Measured Values Theoretical Values Table 1c2 Supply voltage (volt) V1 V2 V3 Σ Voltage Supply current I1 I2 I3 I Total Total resistance R1 R2 R3 Σ R R1+R2+R3 Table 1d1 Supply current (ampere) I1 (amperes) I2 (amperes) I3 (amperes) Σ Current Supply voltage (volt) V1 V2 V3 Equivalent resistance R1 R2 R3 Equivalent resistance Total conductance G1 (Siemens) G2 (siemens) G3 (siemens) Σ G Table 1d2
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